Optimal multiple reinsurance strategy based on Lundberg exponent

Assume that several reinsurers participate in a reinsurance treaty for some loss, and these reinsurers adopt a kind of combined premium principle(the expected premium principle, variance premium principle and exponential premium principle as special cases). Based on the Lundberg exponent, we study the minimal probability of ruin with the Cramer Lundberg jump risk model. Among the class of plausible reinsurance treaties, we derive the optimal multiple reinsurance strategy with nontrivial curved structures, which are different of conventional reinsurance strategy such as proportional and excess of loss reinsurance strategies, etc. Finally, the corresponding numerical and sensitive analyses are given under some two-dimensional reinsurance spaces. This is a joint work with Prof. Ming Zhou.